Question

A music shop sells only guitars and ukuleles.
There were 12 string guitars, 6 string guitars and 4 string ukuleles.
If there were EXACTLY 85 instruments in the shop, at least 8 of each type of instrument,and twice as many guitars as ukuleles, how many of each of 3 instrument types may be in stock?

Answer 1

Let 12 string guitars = a

Let 6 string guitars = b

Let ukuleles = c

c must be odd as (a + b)  = 2c and a + b + c = 85

Start off with 85/3 = 28 1/3, then round down to the next odd number (27).

If c = 27, (a +b) = 58 then solve for a and b, e.g a = 29, b = 29

There the answer could be

12 string guitars x 29

6 string guitars x 29

ukuleles x 27